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<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Assist. Prof. Feza Arslan<o:p></o:p></span></font></b></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;margin-bottom:
12.0pt;text-align:center'><font size=3 face=Tahoma><span style='font-size:12.0pt;
font-family:Tahoma'>(Middle<b><span style='font-weight:bold'> </span></b>East
Technical<b><span style='font-weight:bold'> </span></b>University)<br>
6 November Friday, at <font color=blue><span style='color:blue'>14:00</span></font>;<br>
Bilgi Üniversitesi Dolapdere Kampüsü, Room:<font color=blue><span
style='color:blue'>130.</span></font></span></font><font color=red><span
style='color:red'><o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Title: </span></font></b><o:p></o:p></p>
<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><font
size=3 face=Arial><span style='font-size:12.0pt;font-family:Arial'>Hilbert
Functions of One-dimensional Local Rings <o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'> Abstract:</span></font></b><font
size=2 face=CMBX10><span style='font-size:10.0pt;font-family:CMBX10'><o:p></o:p></span></font></p>
<p class=MsoNormal style='text-align:justify;text-indent:35.4pt;text-autospace:
none'><font size=3 face=Arial><span style='font-size:12.0pt;font-family:Arial'>In
general, very little is known about the Hilbert functions of local rings,even
in dimension 1 case. In the first part of this talk, the preliminaries will be
explained in detail and some open problems will be mentioned, including Rossi's
conjecture, which is open even for Gorenstein local rings corresponding to
monomial curves. In the second part, some partial results supporting Rossi's
conjecture in the monomial curve case will be presented. These results based on
the tool of gluing provide infnitely many families of monomial curves with the
corresponding local Gorenstein rings having nondecreasing Hilbert functions.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
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